Not applicable.
1. Field of the Invention
The present invention generally relates to acoustic well logging. More particularly, the present invention relates to determining slow and fast shear wave velocities and orientations in an anisotropic earth formation.
2. Description of the Related Art
It is a well known phenomena that certain earth formations exhibit a property called xe2x80x9canisotropyxe2x80x9d, wherein the velocity of acoustic waves polarized in one direction may be somewhat different than the velocity of acoustic waves polarized in a different direction within the same earth formation. See, for example, S. Crampin, A Review of the Effects of Anisotropic Layering on the Propagation of Seismic Waves, Geophys. J. R. Astr. Soc., vol. 49, pp 9-27, 1977, incorporated herein by reference as if reproduced in full below. Anisotropy may arise from intrinsic structural properties, such as grain alignment, crystallization, aligned fractures, or from unequal stresses within the formation. Anisotropy is particularly of interest in the measurement of the velocity of shear/flexural waves propagating in the earth formations. Shear or S waves are often called transverse waves because the particle motion is in a direction xe2x80x9ctransversexe2x80x9d, or perpendicular, to the direction that the wave is traveling.
Acoustic waves travel fastest when the direction of particle motion (polarization direction) is aligned with the material""s stiffest direction. If the formation is anisotropic, meaning that there is one direction that is stiffer than another, then the component of particle motion aligned in the stiff direction travels faster than the wave component aligned in the other, more compliant direction in the same plane. A shear wave induced into an anisotropic formation splits into two components, one polarized along the formation""s stiff (or fast) direction, and the other polarized along the formation""s compliant (or slow) direction. Generally, the orientation of these two polarizations is substantially orthogonal (components which are at a 90xc2x0 angle relative to each other). The fast wave is polarized along the direction parallel to the fracture strike and a slow wave in the direction perpendicular to it.
Acoustic well logging techniques have been devised for determining the amount of anisotropy from the shear wave velocities (slowness), and the amount of anisotropy is generally defined as the difference between the velocities of the fast and the slow shear waves. One method of determining fast and slow shear wave velocities and orientations uses an acoustic logging tool 100, as shown in FIG. 1, to detect components of the acoustic signals at several levels of dipole receivers. See, for example U.S. Pat. No. 5,712,829 (hereinafter xe2x80x9cthe ""829 patentxe2x80x9d) issued to Tang et al., incorporated herein by reference as if reproduced in full below.
In the ""829 patent, two dipole sources X and Y, 102, are oriented orthogonal to each other. Signals detected by the dipole receivers A 104, parallel to the X source, are referred to as XA signals when the X source is triggered. Similarly, signals detected by dipole receivers B 106, parallel to the Y source 102, are referred to as YB signals when the Y source is triggered. Cross-component signals can also be detected by the perpendicular receivers when each source is energized, and these signals are referred to as the XB and YA signals for the X and Y sources respectively. Thus, a total of four sets of signals are created for each dipole receiver pair for each set of firings of the sources X and Y.
Each of the four sets of signals can be represented as a time series, each of which consists of a series of numbers indexed with respect to increasing time from the instant at which the respective source is energized. The abscissa value in each series of numbers represents amplitude of the received signal. It must be understood, however, that the signal received by any particular receiver, regardless of which transmitter was fired, contains information about both the fast and the slow waves. Stated otherwise, the signal received by any particular dipole receiver is a combination of the signal induced by the fast wave and the signal induced by the slow wave. Determining the slowness of the fast and slow waves involves separating the fast and slow signals from the actual received signals. Various solutions to determine the fast and slow waveforms from the received signals incorporating both exist, for example, in U.S. Pat. No. 4,817,061 issued to Alford et al., incorporated herein by reference as if reproduced in full below. Once the fast and slow waveforms are decomposed from the composite received waveforms, prior art acoustic determinations are made as to the slowness of each of the waves. In particular, this slowness determination typically involves determining a coherence/semblance of the decomposed waveforms.
While semblance may create visually pleasing results, determining slowness in this matter is unsuitable for error estimation. Consequently, an improved method to determine fast and slow shear wave velocity and orientation in an anisotropic formation is desired.
The preferred embodiments of the present invention comprise a method and apparatus for determining the slowness and orientation of the fast and slow shear waves in an anisotropic earth formation. The apparatus for making this determination preferably comprises two dipole transmitters, oriented substantially perpendicular to each other, mounted on a tool and designed for imparting acoustic energy into the surrounding formation. The tool further comprises a plurality of dipole receiver pairs, the receiver pairs spaced apart from each other and from the dipole transmitters. The dipole receivers in each dipole receiver pair are preferably oriented substantially perpendicular to each other. The preferred method of operation involves firing each dipole transmitter at each depth level sequentially, and obtaining a plurality of received composite signals with the dipole receivers, as the tool is slowly raised or lowered in the borehole. Each of the received signals is a composite signal containing information about the fast and slow shear waves. Each receiver pair on the same elevation creates four received signals for each set of transmitter firings.
A plurality of transfer functions of the formation are assumed and a series of source waveforms or wavelets are estimated using the received waveforms and the assumed transfer functions. More particularly, the preferred embodiments assume a transfer function for the formation at issue, and then estimate, using each set of received signals, a series of source signals that created the received signals based on the assumed transfer function. An objective function is created which is indicative of the similarity of the estimated source signals. Because the actual source signals are preferably the same, a low value of the objective function indicates that the assumed formation transfer function was close to the actual formation transfer function. The source estimation preferably is repeated using multiple transfer functions (assumed strike angles and slowness values). The values of the objective function calculated are preferably plotted in a starting time verses slowness verses strike angle graph, with the strike angle being the ordinate, the slowness being the abscissa, and the starting time being the Z axis coordinate. Thus, for a series of assumed transfer functions, all at a particular single strike angle, a vertical plane of information is created. The process is repeated for a series of assumed strike angles ranging from xe2x88x9290xc2x0 to +90xc2x0 (for a total of 180xc2x0), and at a plurality of slowness values within each assumed transfer function. From minimas in the graph, the orientations of the fast and slow axis may be determined, the difference in slowness between the fast and slow waves may be determined, and the error of the slowness calculation determined.
The disclosed device comprises a combination of features and advantages which enable it to overcome the deficiencies of the prior art devices. The various characteristics described above, as well as other features, will be readily apparent to those skilled in the art upon reading the following detailed description, and by referring to the accompanying drawings.